Research On Improved Level Set Structure Topology Optimization Method Considering Temperature Field

There are often large thermal stresses in various types of thermal engine equipment and components.Using topology optimization methods to reduce its own weight and volume under the premise of meeting strength and safety has obvious practical value for improving its work efficiency and operating economy.It also promotes consumption reduction,energy conservation,and emission reduction in the energy and power industry.Based on the improved level set topology optimization method based on the reactiondiffusion equation,this paper focuses on the study of the stress-minimum topology optimization problem,and discusses the structural topology optimization considering the temperature field.The specific work is as follows:First,the performance and characteristics of the improved level set method are discussed via compliance-minimum topology optimization model..Numerical examples show that both the time step and the diffusion coefficient have a certain range of values,otherwise the optimization will converge to a singular solution or even fail to converge.Then,a stress-minimum topology optimization model with p-norm stress function as the objective function is established.A sensitivity smoothing mechanism is introduced for the instability of stress optimization.Finally,a numerical example is used to verify the effectiveness of the method.For L-beams with geometric singular points,the influence of different parameters p on the optimization results is discussed.It is found that the algorithm can obtain a complete 0-1 distribution optimization structure when the p value is2 and 4.However,when the p value is greater than 4,it will lead to a singular solution with a discontinuous structure.This problem is solved by using the smooth Heaviside function,but this will also lead to the inability to obtain 0-1 distribution optimization structure and other shortcomings.Then,considering the temperature field,stress-minimum structural topology optimization model and compliance-minimum structural topology optimization model are established and the corresponding sensitivity formula is derived.Through numerical examples,the optimization situations of the two models under the action of uniform temperature field and non-uniform temperature field are respectively discussed.For a uniform temperature field,when the heat-mechanical load ratio is around 1,there is a big difference between the minimum stress structure and the minimum compliance structure;for the non-uniform temperature field,the optimization result is mainly affected by the temperature field distribution The two are very different.Whether it is a uniform temperature field or a non-uniform temperature field,there is a big difference between the minimum stress structure and the minimum compliance structure.The optimization of the minimum stress shows better numerical stability.Therefore,for thermoelastic structures,structural topology optimization considering stress is more appropriate.